DIP: Graphical Model Construction by System Decomposition: Increasing the Utility of Algebra Story Problem Solving

网络学习和未来学习技术计划资助的工作将有助于设想下一代学习技术，并推进我们对人们如何在技术丰富的环境中学习的了解。开发和实施（DIP）项目建立在概念验证工作的基础上，展示了所提议的新型学习技术的可能性，PI团队建立并完善了他们所提议的创新的最小可行示例，使他们能够了解未来应该如何设计和使用此类技术，并使他们能够回答有关人们如何学习，如何促进或评估学习，以及/或如何为学习设计的问题。该项目研究了一种新的学习技术，它可能会消除STEM教育中一个臭名昭著的瓶颈：数学模型构建。如今，计算机可以解决复杂的数学问题，但人类仍然必须为计算机定义问题，这被称为构建系统模型。许多学生可以学习程序技能，比如解二次方程，但构建模型会让他们感到沮丧，因为没有程序。这有效地阻止了他们在数学方面的进步，并阻碍了他们进入STEM专业。这也许就是为什么模型构建是同时出现在数学（CCSSM）和科学（NGSS）标准中的少数实践之一。解决这些问题的关键创新是一种基于两个理念的新型学习技术。首先，它强调将给定的系统描述分解为子系统。其次，尽管最终模型是一组代数方程，但该模型首先被构造为一个节点链接图，该图显示了哪些数量与哪些关系相连接。这种符号被称为TopoMath。TopoMath建立在先前成功的Dragoon智能辅导系统的基础上，并代表了该系统的修订，以支持新的图形表示，允许学习者识别不同的问题解决模式。使用贝叶斯知识追踪的隐形评估将允许对学生提交的模型进行反馈，以回应建模中的单词问题。当将模型表示为TopoMath图时，通常可以绘制出不同的子系统对应于不同的子图。这使得学生更容易理解模型和它所代表的系统之间的关系。此外，当通过将系统分解为子系统来构建模型时，TopoMath图中的空白区域表明哪些子系统仍然需要建模。学生可以通过比较和概括具有视觉上相似的TopoMath模型的系统来学习模型构建模式，以便在通过将系统分解为子系统来构建模型时，如果模式与子系统匹配，则可以填充模型的整个部分，而无需进一步分解。这些只是将系统分解和TopoMath的数学模型的图形表示相结合的一些协同作用。该项目将探索TopoMath学习活动的序列，目标是让学生在20小时的教学中掌握模型构建。该指导将在大学数学补习班的背景下进行，相当于高中代数2课程。教学将包括使用TopoMath技术的个人、小组和全班活动。将使用知识-学习-教学框架对口头协议进行定性分析，以进行系统评估，并更好地理解由系统表示和建模支架支持的模型构建中的学习过程。

The Cyberlearning and Future Learning Technologies Program funds efforts that will help envision the next generation of learning technologies and advance what we know about how people learn in technology-rich environments. Development and Implementation (DIP) Projects build on proof-of-concept work that shows the possibilities of the proposed new type of learning technology, and PI teams build and refine a minimally-viable example of their proposed innovation that allows them to understand how such technology should be designed and used in the future and that allows them to answer questions about how people learn, how to foster or assess learning, and/or how to design for learning. This project studies a new genre of learning technology that may remove a notorious bottleneck in STEM education: mathematical model construction. These days, computers can solve complex mathematical problems, but humans must still define the problem for the computer, which is called constructing a model of a system. Many students can learn procedural skills, such as solving a quadratic equation, but constructing a model frustrates them because there is no procedure. This effectively stops their progress in math and blocks their entry to STEM professions. That may be why model construction is one of the few practices that appears in both math (CCSSM) and science (NGSS) standards. The key innovation for solving these problems is a new genre of learning technology based on two ideas. First, it emphasizes decomposing the given system description into subsystems. Second, although the final model is a set of algebraic equations, the model is first constructed as a node-link graph that shows which quantities are connected to which relationships. This notation is called TopoMath.TopoMath builds on prior success with the Dragoon intelligent tutoring system, and represents a revision of that system to support a novel graphical representation to allow learners to recognize distinct problem-solving schemata. Stealth assessment using Bayesian Knowledge Tracing will allow feedback on student submitted models in response to word problems in modelling. When a model is represented as a TopoMath graph, it can usually be drawn such that distinct subsystems correspond to distinct subgraphs. This makes it easier for students to understand the relationship between the model and the system that is represents. Moreover, when constructing a model by decomposing a system into subsystems, blank areas in the TopoMath graph suggest which subsystems still need to be modeled. Students can learn model construction schemas by comparing and generalizing systems that have visually similar TopoMath models so that when constructing a model by decomposing a system into subsystems, if a schema matches a subsystem, then a whole section of the model can be filled in without further decomposition. These are just a few of the synergies of combining system decomposition and TopoMath's graphical representation of mathematical models. This project will explore sequences of TopoMath learning activities with the goal of bringing students to model construction mastery with just 20 hours of instruction. The instruction will be developed in the context of remedial college math classes that are equivalent to high school algebra 2 classes. The instruction will include individual, small group and whole class activities using the TopoMath technology. Qualitative analysis of verbal protocols will be undertaken using the Knowledge-Learning-Instruction framework both for system evaluation, and to better understand the processes of learning in model construction that are supported by the system's representations and scaffolds for modeling.